Probability & Statistics Honors Unit Test #2

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 1 Describe the distribution shown above. (5)

The distribution of heart rates is skew left, is centered near 85bpm, and has a range of approximately 60bpm. There are no obvious unusual features.

 2 Zeke’s score on a reasoning test says he is in the 67th percentile. Interpret this score. (3)

This means that Zeke’s score is as high or higher than 67% of all other scores on this reasoning test.

 28 50 193 55 4 7 147 76 10 0 6 26 10 84 0 9 1 0 62 26 15 226 41 55 54 46 128 4 105 40 4 273 164 7

 3 The data above are the number of successful demands between failures (how many times the item started successfully before failing to start) for the diesel backup generators at a nuclear power plant. Determine if there are any outliers in these data. (5)

My calculator tells me that ${Q}_{1}=7$ and ${Q}_{3}=76$, so $IQR=69$. The lower bound for outliers is $7-1.5\left(69\right)=-96.5$, and the upper bound for outliers is $76+1.5\left(69\right)=179.5$. There are no negative data, but there are three data that are above the upper bound (193, 226 and 273) so there are outliers in this data set.

The amount of fluoride in drinking water was measured each day over a period of 25 days. The data collected are shown below (the units are parts per million).

 0.75 0.86 0.84 0.85 0.97 0.94 0.89 0.84 0.83 0.89 0.88 0.78 0.77 0.76 0.82 0.72 0.92 1.05 0.94 0.83 0.81 0.85 0.97 0.93 0.79

Use these data for the next eight questions.

 4 Find the mean of the data. (2)

0.8592

 5 Find the median of the data. (2)

0.85

 6 Find the range of the data. (2)

0.33

 7 Find the standard deviation of the data. (2)

0.0795

 8 Find $Q{\text{ }}_{1}$ for these data. (2)

0.8

 9 Find $Q{\text{ }}_{3}$ for these data. (2)

0.925

 10 Find the interquartile range for these data. (2)

0.125

Since the data are skew right, the better measures of center and spread would be the median and interquartile range.

An animal scientist added antibiotics to the diet of chicks to promote growth. The mass gain (grams) of a sample of the chicks is given below.

 4.9 3.8 4.3 4.3 3.9 3.8 4.7 3.9 4 4.2 4.3 4.7 4.1 4 4.6 4.4 4.6 4.4 4.9 4.4 4 3.9 4.5 4.3 3.8 4.1 4.3 4.2 4.5 4.4

 12 Construct a boxplot of the data given above. (5)

Company officials were concerned about the length of time a particular drug product retained its potency. A random sample of 10 bottles of the product was drawn from the production line and analyzed for potency. A second sample of 10 bottles was obtained and stored in a regulated environment for a period of one year. The readings obtained from each sample are given in the tables below.

Fresh

 10.2 10.6 10.5 10.7 10.3 10.2 10.8 10 9.8 10.6

Stored

 9.8 9.7 9.6 9.5 10.1 9.6 10.2 9.8 10.1 9.9

 13 Compare the distributions of these two samples. (5)

First, the graphs:

The fresh sample appears to have a higher center potency than the stored sample. The amount of variation in the potency of the fresh sample appears to be larger than that of the stored sample. The fresh sample appears to be skew left; the stored sample is likely symmetric. Neither data set has any unusual features.

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